Three Non-Colinear Points

Steps

1. Construct the segment bisector of the segment CB.
2. Construct the segment bisector of the segment AC.
3. Construct the segment bisector of the segment AB.
4. Name the point of intersection of all three aforementioned bisectors S. This intersection is the center of the circle we are looking for.
5. Construct a circle with the center S and the radius SA.

Steps

1. Choose the circle for a circular inversion: the center of this circle is one of the specified points from the assignment. The circle's radius is chosen in a way that another of the specified points lies on the circle and is therefore a fixed point. However, this is not strictly necessary.
2. In a circular inversion, point A is displayed to infinity, point B is fixed, point C is displayed to C'.
3. The projection of the solution in the circular inversion is the line p passing through the projection of all three points (the projection of the point A is at infinity).
4. We project the line p in the circular inversion. Its image is the desired circle k.